Does submodularity property hold for the trace of a positive-definite hermitian matrix? 

I.e., does given any real symmetric positive-definite matrices $X,A,B$
$$
tr~X^{-1} + tr~(X+A+B)^{-1} \geq tr~(X+A)^{-1} + tr~(X+B)^{-1}
$$
hold?